{
 "cells": [
  {
   "cell_type": "raw",
   "id": "8c69730d",
   "metadata": {},
   "source": [
    "---\n",
    "title: Calculus Problem Generator\n",
    "description: Generates Derivative and Integral Expressions at https://nsc9.github.io/\n",
    "show-code : False\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c5197005",
   "metadata": {},
   "outputs": [],
   "source": [
    "# recent change: Added useful links, Added plaintext version of expressions for easy copy/paste to a solver."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bdf2faf",
   "metadata": {},
   "source": [
    "# Solve with pen and paper:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "108761f9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from sympy.simplify.fu import TR22,TR2i\n",
    "from sympy import ln,exp,Function,Derivative,Eq,Integral,factor_terms, sqrt, Symbol,Limit\n",
    "from sympy import sin,cos,tan,Rational,nsimplify\n",
    "import random\n",
    "f = Function('f')\n",
    "g = Function('g')\n",
    "h = Function('h')\n",
    "theta = Symbol('theta')\n",
    "i = 0\n",
    "dkeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\",\"li\",\"erf\",\"Si\",\"Ci\",\"hyper\",\"fresnel\",\"Li\",\"expint\",\"zoo\",\n",
    "\"nan\",\"oo\",\"abs\",\"re\",\"EulerGamma\", \"sinh\",\"tanh\", \"cosh\",'sign','abs','atan','csc','asin'} \n",
    "ikeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\", \"li\", \"erf\", \"atan\", \"Si\",  \"Ci\",  \"hyper\",  \"fresnel\",  \"Li\", \n",
    "\"expint\",\"zoo\", \"nan\", \"oo\",\"EulerGamma\",\"sinh\",\"csc\",\"asin\"}\n",
    "keywords2 = {\"sin\",\"cos\",\"tan\"}\n",
    "def random_variable(i):\n",
    "    return Symbol(random.choice([i for i in ['v','t','x','z','y']]), real=True)\n",
    "def random_value(i):\n",
    "    return random.choice([i for i in range(-10,10) if i not in [0]])\n",
    "def power(a):      \n",
    "    return random_value(i)*a**int(random_value(i)/2)\n",
    "def scalar(a):       \n",
    "    return a*random_value(i) + random_value(i)\n",
    "def addSUBTR(a):     \n",
    "    return a+random_value(i)\n",
    "def dmain(a):\n",
    "    def random_math(a): \n",
    "        funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt]   \n",
    "        operations = [f(a)*g(a)+h(a), f(a)-g(a)*h(a),f(a)/(g(a)-h(a)), f(a)/(-g(a)+h(a)),\n",
    "                      f(a)+g(a)+h(a), f(a)-g(a)-h(a),f(a)+g(a)-h(a), f(a)-g(a)+h(a),\n",
    "                      (f(a)*g(a))/h(a), f(a)/(g(a)*h(a)),f(g(h(a))),f(h(a))+g(a),f(h(a))-g(a),\n",
    "                      f(h(a))/g(a),f(a)/g(h(a)),f(h(a))*g(a),f(a)*h(a)*g(a)]\n",
    "        operation = operations[random.randrange(0,len(operations))]\n",
    "        return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
    "    [random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
    "    return random_math(a)\n",
    "def imain(a):\n",
    "    def random_math2(a):  \n",
    "        funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt]   \n",
    "        operations = [f(g(a)),f(a)+g(a),f(a)-g(a),f(a)/g(a),f(a)*g(a),\n",
    "                     f(g(a))**2,2*f(a)+g(a),2*f(a)-g(a),2*f(a)/g(a),2*f(a)*g(a)]\n",
    "        operation = operations[random.randrange(0,len(operations))]\n",
    "        return [[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
    "    [random.randrange(0,len(funs))]\n",
    "    return random_math2(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5ddcf6a5",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a' = \\frac{d}{d \\theta} \\left(- 3 \\theta + \\tan{\\left(\\theta \\right)} - 14\\right)$"
      ],
      "text/plain": [
       "Eq(a', Derivative(-3*theta + tan(theta) - 14, theta))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle B = \\int 3 \\log{\\left(x \\right)}\\, dx$"
      ],
      "text/plain": [
       "Eq(B, Integral(3*log(x), x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "derror = True\n",
    "def dtest():\n",
    "    global setup1\n",
    "    global derror\n",
    "    global practice1\n",
    "    a = random_variable(i)\n",
    "    setup1 = dmain(a)\n",
    "    practice1 = Derivative(setup1,a)       \n",
    "    p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
    "    if any(kw in str(setup1) for kw in keywords2):\n",
    "        setup1 = setup1.replace(a,theta)\n",
    "        practice1 = Derivative(setup1,theta)   \n",
    "        p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
    "    if p1eq.rhs != 0 and not any(kw in str(p1eq) for kw in dkeywords):\n",
    "        derror = False\n",
    "    return p1eq\n",
    "while derror == True: \n",
    "    output1 = dtest()\n",
    "ierror = True\n",
    "def itest():\n",
    "    global ierror\n",
    "    global practice2\n",
    "    global setup2\n",
    "    a = random_variable(i)\n",
    "    setup2 = imain(a)\n",
    "    practice2 = Integral(setup2,a)  \n",
    "    p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
    "    if str(factor_terms(p2eq.lhs)) != str(factor_terms(p2eq.rhs)) and not any(kw in str(p2eq) for kw in ikeywords)\\\n",
    "    and str(p2eq.lhs) != str(-p2eq.rhs): \n",
    "        if any(kw in str(setup2) for kw in keywords2):\n",
    "            setup2 = setup2.replace(a,theta)\n",
    "            practice2 = Integral(setup2,theta)  \n",
    "            p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
    "        ierror = False\n",
    "    return p2eq\n",
    "while ierror == True:\n",
    "    output2 = itest()\n",
    "a1 = Symbol(\"a'\")\n",
    "B = Symbol('B')\n",
    "eq1 = Eq(a1,nsimplify(output1.lhs))\n",
    "eq2 = Eq(B,nsimplify(output2.lhs))\n",
    "eq3 = Eq(a1,nsimplify(output1.rhs))\n",
    "eq4 = Eq(B,nsimplify(output2.rhs))\n",
    "def lhs():\n",
    "    display(eq1,eq2) \n",
    "    return\n",
    "def rhs():\n",
    "    return display(eq3,eq4)\n",
    "lhs()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2393180e",
   "metadata": {},
   "source": [
    "___________________________________________________________________________________________________________________\n",
    "If LaTeX display breaks, refresh the page. Runtime is under a second if you run the Jupyter-Notebook locally.\n",
    "\n",
    "**Created by GitHub.com/NSC9  - https://nsc9.github.io/ - MIT License - v7.5**\n",
    "\n",
    "Latest version source code: https://github.com/NSC9/Sample_of_Work/tree/Main/Artificial_Calculus_Teacher\n",
    "\n",
    "Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "15c3f34f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Derivative(-3*theta + tan(theta) - 14, theta)\n",
      "Integral(3*log(x), x)\n"
     ]
    }
   ],
   "source": [
    "print(eq1.rhs)\n",
    "print(eq2.rhs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30b55c90",
   "metadata": {},
   "source": [
    "https://www.derivative-calculator.net/\n",
    "\n",
    "https://www.integral-calculator.com/\n",
    "___________________________________________________________________________________________________________________\n",
    "\n",
    "# Answers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fbec286d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a' = \\sec^{2}{\\left(\\theta \\right)} - 3$"
      ],
      "text/plain": [
       "Eq(a', sec(theta)**2 - 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle B = 3 x \\log{\\left(x \\right)} - 3 x$"
      ],
      "text/plain": [
       "Eq(B, 3*x*log(x) - 3*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rhs()"
   ]
  }
 ],
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